Those who run religious spaces can still refuse to marry gay couples if it is against their church's beliefs. Part of Justice Kennedy's speech included the assertion that religious institutions would be protected under the First Amendment:

"It must be emphasized that religions, and those who adhere to religious doctrines, may continue to advocate with utmost, sincere conviction that, by divine precepts, same-sex marriage should not be condoned. The First Amendment ensures that religious organizations and persons are given proper protection as they seek to teach the principles that are so fulfilling and so central to their lives and faiths and to their own deep aspirations to continue the family structure they have long revered."

In other words, while churches in every state are now legally allowed to perform gay marriages, they are not legally obligated to perform those marriages. It is up to each individual sect, or in some cases, individual pastors, to decide whether they will perform such marriages. For example, the Presbyterian Church recognized same-sex marriage in March, but they have left it up to individual pastors to decide whether to officiate such weddings. The Evangelical Lutheran Church of America has a similar policy.

There are many churches that more universally accept gay marriage. Gay couples have been legally allowed to get married in the United Church of Christ since 2005. The Community of Christ also supports same sex marriage, and the Unitarian Universalist Church has long supported the LGBTQ community and performs marriages. For an idea of which specific churches marry gay couples, the website engaygedweddings.com is a helpful resource, though thanks to this incredible SCOTUS decision, the website will now have to expand its directory.